Geodesic
On the $K^2$ of degenerations of surfaces and the multiple point formula
Alberto Calabri 1   ; Ciro Ciliberto 2   ; Flaminio Flamini 2   ; Rick Miranda 3
1 Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università degli Studi di Padova, 35121 Padova, Italy
2 Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, 00133 Roma, Italy
3 Department of Mathematics, Colorado State University, Fort Collins, CO 80523, United States
Annals of mathematics, Tome 165 (2007) no. 2, pp. 335-395 Cet article a éte moissonné depuis la source Annals of Mathematics website

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In this paper we study some properties of reducible surfaces, in particular of unions of planes. When the surface is the central fibre of an embedded flat degeneration of surfaces in a projective space, we deduce some properties of the smooth surface which is the general fibre of the degeneration from some combinatorial properties of the central fibre. In particular, we show that there are strong constraints on the invariants of a smooth surface which degenerates to configurations of planes with global normal crossings or other mild singularities.

DOI : 10.4007/annals.2007.165.335

Alberto Calabri  1   ; Ciro Ciliberto  2   ; Flaminio Flamini  2   ; Rick Miranda  3

1 Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università degli Studi di Padova, 35121 Padova, Italy
2 Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, 00133 Roma, Italy
3 Department of Mathematics, Colorado State University, Fort Collins, CO 80523, United States 
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Alberto Calabri; Ciro Ciliberto; Flaminio Flamini; Rick Miranda. On the $K^2$ of degenerations of surfaces and the multiple point formula. Annals of mathematics, Tome 165 (2007) no. 2, pp. 335-395. doi: 10.4007/annals.2007.165.335

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